From the evidence below, failing very strong evidence that it was routine for merchant European slave traders to hunt down slaves themselves along the Slave Coast, the percentage of slaves delivered to the New World that were purchased from black slavers must be very close to 100%. There is simply no business model, consistent with the slave trade as we understand it, that supports or includes the practice of idling for weeks and months of slave hunting along the African coast instead of just purchasing the abundant slaves to be had there.
There is, just on its own, overwhelming circumstantial evidence that your premise is true:
The well documented system of Triangular Trade between Europe, the Slave Coast, and the West Indies and American slave markets.
The only point of carrying commodities and specie to the Slave Coast was to use in purchase of, or barter for, slaves. No merchant could make a profit carrying these items thousands of kilometres just to dump them - that the slave ships arrived at the Slave Coast with these items and left with them replaced by slaves leads to a self-evident conclusion.
Sub-saharan Africa was a very unfriendly place for Europeans prior to the late 19th Century. Not only unfriendly natives quite capable, in numbers, of overwhelming a small ship's crew, but also diseases to which Europeans had little resistance. Extended stays on the coast accompanied by frequent visits into the jungle would have resulted in crew losses that could be ill afforded.
Further merchant ships' crews were few in number - the bare minimum needed to maneuver the vessel in a sea-worthy manner and perhaps a passenger or two. It would not have been possible for such crews, of a dozen or two, to capture slaves except by the handful from the coastal tribes - after which the unfavourable numbers would have required them to move to another such location, and another, and another, in order to fill a ship with 400-500 slaves. The logistics are untenable, and the second ship to attempt such would be lucky to escape alive.
Combined, these two factors make it completely untenable for any large scale attempt by European merchants to "self-harvest" the millions of slaves that were transported to the New World prior to Britain's enforcement of a ban on the Slave Trade in the 19th Century.
Britain arrange treaties with Portugal Sweden and Denmark, 1810–1814, whereby they agreed to end or restrict their trading. These were preliminary to the Congress of Vienna negotiations that Castlereagh dominated and which resulted in a general declaration condemning the slave trade. ... Eventually, in , an arrangement was reached between London and Washington. With the arrival of a staunchly anti-slavery government in Washington in 1861, the Atlantic slave trade was doomed. In the long run, Castlereagh's strategy on how to stifle the slave trade proved successful.
The Royal Navy's West Africa Squadron, established in 1808, grew by 1850 to a force of some 25 vessels, which were tasked with combating slavery along the African coast. Between 1807 and 1860, the Royal Navy's Squadron seized approximately 1,600 ships involved in the slave trade and freed 150,000 Africans who were aboard these vessels.
But beyond all this circumstantial evidence is the [direct history and accounts of the participants]4. While it was taking place there was no public shame in this trade - and no guile or deception involved in it until after 1808.
As of 1778, Thomas Kitchin estimated that Europeans were bringing an estimated 52,000 slaves to the Caribbean yearly, with the French bringing the most Africans to the French West Indies (13,000 out of the yearly estimate). The Atlantic slave trade peaked in the last two decades of the 18th century, during and following the Kongo Civil War. Wars among tiny states along the Niger River's Igbo-inhabited region and the accompanying banditry also spiked in this period. Another reason for surplus supply of enslaved people was major warfare conducted by expanding states, such as the kingdom of Dahomey, the Oyo Empire, and the Asante Empire.